{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9c0d3c02",
   "metadata": {},
   "source": [
    "# 使用最小二乘法拟合曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "770cd858",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 举例：我们用目标函数$y=sin2{\\pi}x$, 加上一个正态分布的噪音干扰，用多项式去拟合\n",
    "# 最小二乘法拟合曲线\n",
    "import numpy as np\n",
    "# SciPy 是一个基于 NumPy 的科学计算库，提供了更多的数学、科学和工程计算功能。\n",
    "import scipy as sp\n",
    "# leastsq 函数是用于最小二乘法拟合的函数\n",
    "from scipy.optimize import leastsq\n",
    "import matplotlib.pyplot as plt\n",
    "# 这是一个 Jupyter Notebook 的魔法命令，用于在 Notebook 中显示 Matplotlib 绘制的图形，并将其嵌入到 Notebook 内部。\n",
    "# 这使得图形能够直接在 Notebook 中显示，而不是弹出一个新窗口。\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7a2fce43",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 目标函数，用于生成真实的数据。在这个例子中，它定义了一个正弦函数 sin(2𝜋𝑥)，用于产生模拟数据。\n",
    "def real_func(x):\n",
    "    return np.sin(2 * np.pi * x)\n",
    "# 多项式函数，用于拟合数据。它接受一个多项式的系数 p 和输入数据 x，并返回使用这些系数计算出的拟合函数的值。\n",
    "def fit_func(p, x):\n",
    "#     np.poly1d() 函数是 NumPy 库中用于创建一维多项式对象的函数。它将系数数组作为输入，并返回一个多项式对象，\n",
    "#     可以用于进行多项式运算，如求导、积分、求根等操作。\n",
    "#     np.poly1d(coeffs)\n",
    "#     参数说明：\n",
    "#     coeffs：多项式的系数数组，从最高次幂到常数项的顺序排列。\n",
    "    f = np.poly1d(p)\n",
    "    return f(x)\n",
    "    #  残差函数，用于计算拟合函数与真实数据之间的残差。它接受一个多项式的系数 p、输入数据 x 和真实数据 y，并返回拟合函数的值与真实数据的差值。\n",
    "def residuals_func(p, x, y):\n",
    "    return fit_func(p, x) - y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5c179730",
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)\n",
    "# start：起始值，生成的数据点的起始值。\n",
    "# stop：结束值，生成的数据点的结束值。\n",
    "# num：数据点的个数，默认值为 50。\n",
    "# endpoint：布尔值，控制是否包含结束值。如果为 True（默认值），则最后一个数据点等于结束值；如果为 False，则不包含结束值。\n",
    "# retstep：布尔值，控制是否返回步长。如果为 True，则返回 (数组, 步长) 的元组；如果为 False（默认值），则只返回数组。\n",
    "# dtype：数据类型，指定返回数组的数据类型。\n",
    "\n",
    "# 十个点\n",
    "x = np.linspace(0, 1, 10)\n",
    "x_points = np.linspace(0, 1, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1b1ba237",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 加上正态分布噪音的目标函数的值\n",
    "y_ = real_func(x)\n",
    "# np.random.normal() 函数是 NumPy 库中用于生成服从正态分布（也称为高斯分布）的随机数的函数。\n",
    "# np.random.normal(loc=0.0, scale=1.0, size=None)\n",
    "# 参数说明：\n",
    "# loc：正态分布的均值（也称为期望值），默认值为 0.0。\n",
    "# scale：正态分布的标准差，控制分布的分散程度，默认值为 1.0。\n",
    "# size：生成随机数的个数或数组的形状，默认为 None，表示返回单个随机数。\n",
    "y = [np.random.normal(0, 0.1) + y1 for y1 in y_]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8c19c2ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 拟合函数\n",
    "def fitting(M = 0):\n",
    "#     M为多项式的系数\n",
    "# 随机初始化多项式参数\n",
    "    p_init = np.random.rand(M + 1)\n",
    "#     使用最小二乘法拟合函数\n",
    "# leastsq 函数是 SciPy 库中的一个函数，用于通过最小二乘法（Least Squares）拟合一个函数模型到一组观测数据上。\n",
    "# 最小二乘法是一种常用的参数估计方法，通过最小化观测数据与理论模型之间的残差平方和来找到最优的参数值。\n",
    "# 这个函数的基本语法如下：\n",
    "# leastsq(func, x0, args=(), Dfun=None, full_output=0, col_deriv=0, ftol=1.49012e-8, xtol=1.49012e-8, gtol=0.0, maxfev=0, epsfcn=None, factor=100, diag=None)\n",
    "# 参数说明：\n",
    "# func：用于计算残差的函数，该函数的参数列表应该包括待优化的参数以及输入数据。\n",
    "# x0：待优化的参数的初始值，可以是一个数值或者一个数组。\n",
    "# args：传递给 func 函数的额外参数，以元组的形式传递。\n",
    "# Dfun：可选参数，用于计算残差函数的雅可比矩阵（Jacobian 矩阵）。\n",
    "# full_output：可选参数，如果为 1，则返回一个字典，其中包含了拟合结果以及其他详细信息；如果为 0（默认值），则只返回拟合结果。\n",
    "# 其他参数是控制算法收敛性和终止条件的参数，一般情况下使用默认值即可。\n",
    "# leastsq 函数通过调用指定的残差函数（通常是定义为观测数据与理论模型之间的差值），利用最小二乘法优化待估计的参数值，使得残差的平方和最小化。它返回一个包含估计的参数值的数组，以及一个表示优化结果的状态码。\n",
    "    p_lsq = leastsq(residuals_func, p_init, args = (x, y))\n",
    "    print('Fitting Parameters: ', p_lsq)\n",
    "    \n",
    "#     可视化\n",
    "    plt.plot(x_points, real_func(x_points), label = 'real')\n",
    "    plt.plot(x_points, fit_func(p_lsq[0], x_points), label = 'fitted curve')\n",
    "    plt.plot(x, y, 'bo', label = 'noise')\n",
    "    plt.legend()\n",
    "    return p_lsq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "38c7c53c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters:  (array([-0.06905272]), 1)\n",
      "(array([-0.06905272]), 1)\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M = 0\n",
    "print(fitting(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2104908a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters:  (array([-1.41561458,  0.63875457]), 1)\n",
      "(array([-1.41561458,  0.63875457]), 1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M = 1\n",
    "print(fitting(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "28949a03",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters:  (array([ 21.29979534, -32.01259792,  10.76976643,  -0.10685389]), 1)\n",
      "(array([ 21.29979534, -32.01259792,  10.76976643,  -0.10685389]), 1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M = 3\n",
    "print(fitting(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f721987c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters:  (array([-2.95862195e+04,  1.27650238e+05, -2.30145890e+05,  2.25192340e+05,\n",
      "       -1.30003345e+05,  4.50782728e+04, -9.10270046e+03,  9.48629912e+02,\n",
      "       -3.13908518e+01, -1.17828115e-01]), 2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M = 9\n",
    "p_lsq_9 = fitting(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90280f57",
   "metadata": {},
   "source": [
    "# 正则化"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84ad9601",
   "metadata": {},
   "source": [
    "结果显示过拟合， 引入正则化项(regularizer)，降低过拟合\n",
    "\n",
    "$Q(x)=\\sum_{i=1}^n(h(x_i)-y_i)^2+\\lambda||w||^2$。\n",
    "\n",
    "回归问题中，损失函数是平方损失，正则化可以是参数向量的L2范数,也可以是L1范数。\n",
    "\n",
    "- L1: regularization\\*abs(p)\n",
    "\n",
    "- L2: 0.5 \\* regularization \\* np.square(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "8537eea4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x175198d10>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regularization = 0.0001\n",
    "\n",
    "def residuals_func_regularization(p, x, y):\n",
    "    ret = fit_func(p, x) - y\n",
    "    ret = np.append(ret, np.sqrt(0.5 * regularization * np.square(p)))\n",
    "#     print('加入正则化项后的残差值：', ret)\n",
    "    return ret\n",
    "\n",
    "p_init = np.random.rand(10)\n",
    "p_lsq_regularization = leastsq(residuals_func_regularization, p_init, args = (x, y))\n",
    "plt.plot(x_points, real_func(x_points), label = 'real')\n",
    "def fitting_9():\n",
    "    p_init = np.random.rand(10)\n",
    "    p_lsq = leastsq(residuals_func, p_init, args=(x, y))\n",
    "    return p_lsq\n",
    "\n",
    "p_lsq_9 = fitting_9()\n",
    "plt.plot(x_points, fit_func(p_lsq_9[0], x_points), label = 'fitted curve')\n",
    "plt.plot(x_points, fit_func(p_lsq_regularization[0], x_points), label = 'regularization')\n",
    "plt.plot(x, y, 'bo', label = 'noise')\n",
    "plt.legend()"
   ]
  }
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